Pauli Principle Influence in Nuclear Models

The Pauli exclusion principle is involved in the basic explanation of the shell model for nuclear energy states. The evidence for shell structure in the nucleus was surprising at the outset, because a dense collection of strongly interacting particles should be bumping into each other all the time, resulting in redirection and perhaps loss of energy for the particles. The Pauli principle effectively blocks the loss of energy because only one nuclear particle can occupy a given energy state (with spin 1/2, neutrons and protons are fermions.) In this dense collection of matter, all the low energy states will fill up. This means that the particles cannot take part in interactions which would lower their energy, because there are no lower energy states they can go to. Scattering from an external particle which raises the energy of a nucleon can happen, but scattering which lowers an energy level is blocked by the exclusion principle.

The Pauli principle is also invoked in the liquid drop model, and there is a term in the Weizsaecker formula for binding energy which is attributed to the exclusion principle. The filling of all the low energy states is envisioned in the liquid drop model, and that favors the condition A=2Z (i.e., equal numbers of protons and neutrons). Since neutron and proton energy levels for given quantum states are comparable, then an overall lower energy can be obtained by filling them both to the same level rather than having one or more nucleons in higher quantum levels. The Pauli principle also favors even numbers of neutrons and protons: pairs of fermions will be expected to have anti-parallel spin and therefore not contribute to the overall spin. This gives another term in the Weizsaecker formula.